An Embedding Theorem given by the Modulus of Variation

Authors

  • Laszlo Leindler Bolyai Institute, University of Szeged, Aradi vertanuk tere 1, H-6720 Szeged, Hungary

DOI:

https://doi.org/10.26713/jims.v1i1.6

Keywords:

Embedding relation, Bounded variation, Modulus of variation, Continuity

Abstract

In [5] and [6] we extended an interesting theorem of Medvedeva [7] pertaining to the embedding relation $H^\omega\subset \Lambda BV$, where $\Lambda BV$
denotes the set of functions of $\Lambda$-bounded variation. Our theorem proved in [6] unifies the notion of $\varphi$-variation due to Young [8] and that of the generalized Wiener class $BV(p(n)\uparrow)$ due to Kita
and Yoneda [4]. In this note we generalize the theorem proved in [6] such that it will use the concept of the modulus of variation due to Chanturia [2]. For further references pertaining to the new notion mentioned above we refer to an interesting paper by Goginava and Tskhadaia [3]. We also show that our new theorem includes our previous result as a special case.

Downloads

Downloads

CITATION

How to Cite

Leindler, L. (2009). An Embedding Theorem given by the Modulus of Variation. Journal of Informatics and Mathematical Sciences, 1(1), 27–31. https://doi.org/10.26713/jims.v1i1.6

Issue

Vol. 1 No. 1 (2009)

Section

Research Article

License

Authors who publish with this journal agree to the following terms:
  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.